On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes

Tin-Lam Toh, Tuan-Seng Chew

Abstract: The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Ito integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Ito integral, thereby providing a characterization of Henstock-Kurzweil-Ito integrable stochastic processes in terms of their primitive processes.